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A particle located at x = 0 at time t =...

A particle located at `x = 0` at time `t = 0`, starts moving along with the positive ` x-direction` with a velocity 'v' that varies as ` v = a sqrt(x)`. The displacement of the particle varies with time as

A

t

B

`t^(1//2)`

C

`t^(3)`

D

`t^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`v = alphasqrt(x) rArr (dx)/(dt) = alphasqrt(x)`
`rArr int (dx)/(sqrt(x)) = int alpha dt rArr (x^(-1/2+1))/(-1/2+1)=alphat rArr x = 1/4 alpha^(2)t^(2)` .
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